Solve for $x$ and $y$ using elimination. ${-6x-2y = -52}$ ${-5x+2y = -36}$
Solution: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $-2y$ and $2y$ cancel out. $-11x = -88$ $\dfrac{-11x}{{-11}} = \dfrac{-88}{{-11}}$ ${x = 8}$ Now that you know ${x = 8}$ , plug it back into $\thinspace {-6x-2y = -52}\thinspace$ to find $y$ ${-6}{(8)}{ - 2y = -52}$ $-48-2y = -52$ $-48{+48} - 2y = -52{+48}$ $-2y = -4$ $\dfrac{-2y}{{-2}} = \dfrac{-4}{{-2}}$ ${y = 2}$ You can also plug ${x = 8}$ into $\thinspace {-5x+2y = -36}\thinspace$ and get the same answer for $y$ : ${-5}{(8)}{ + 2y = -36}$ ${y = 2}$